Retardation corrections to the quarkonium spectrum and the form of the confinement kernel

We reconsider the problem of the retardation corrections to the quarkonium spectrum, due to some errors occurring in an earlier paper. We find that such corrections are too large (1 GeV) and rule out the significance of the usual confining part Iconf of the BS kernel as obtained by a simple covariantization of the instantaneous form implied by the linear potential. This suggests to keep Iconf instantaneous so that the only retardation correction comes from the perturbative part of the kernel. Under this assumption we calculate the correction to the hyperfine splitting of heavy quarkonium and find it to be of the order of few tens MeV and in the right direction.